Modern Portfolio Analysis - Markowitz Model Introduction, Assumptions and Parameters

Modern Portfolio Analysis - Markowitz Model
Unit 2 SAPM Notes 
Portfolio analysis and Management


Dr. Harry M. Markowitz was the person who developed the first modern portfolio analysis model. Markowitz used mathematical programming and statistical analysis in order to arrange for the optimum allocation of assets within portfolio. He infused a high degree of sophistication into portfolio construction by developing a mean-variance model for the selection of portfolio. Markowitz approach determines for the investors the efficient set of portfolio through three importance variables - Return, standard deviation and coefficient of correlation.

Markowitz model is called the “Full Covariance Model”. Through this method the investor can find out the efficient set of portfolio by finding out the trade off between risk and return, between the limits of zero and infinity. Markowitz theory is based on several assumptions these are:


a)       The markets are efficient and absorb all the information quickly and perfectly. So an investor can earn superior returns either by technical analysis or fundamental analysis. All the investors are in equal category in this regard.

b)      Investors are risk averse. Before making any investments, all of them, have a common goal-avoidance of risk. But practically this assumption does hold good. In a country like India, majority of investors invests money on the basis of market news without doing any technical and fundamental analysis.

c)       Investors are rational. They would like to earn the maximum rate of return with a given level of income or money.

d)      Investors base their decisions solely on expected return and variance (or standard deviation) of returns only.

e)      For a given risk level, investors prefer high returns to lower returns. Similarly, for a given level of expected return, they prefer less risk to more risk.

f)        The investor can reduce the risk if he adds investments to his portfolio.

g)       Investors consider each investment alternative as being represented by a probability distribution of expected returns over some holding period.

h)      A portfolio of assets under the above assumptions is considered to be efficient if no other portfolio of assets offers higher expected return with the same (or lower) risk or lower risk with the same (or higher) expected return.


Based on thorough and scientific research, Markowitz has set down his own guidelines for diversification:

a)       The investments have different types of risk characteristics. Some are systematic or market related risks and the others are unsystematic or company related risks.

b)      His diversification involves a proper number of securities not too less nor too many.

c)       The securities have no correlation or negative correlation.

d)      Last is the proper choice of the companies, securities or assets whose returns are not related and whose risks are mutually off setting to reduce the overall risk.

Markowitz lays down three parameters for building up the efficient set of portfolio:

a)       Expected returns.

b)      Standard deviation from mean to measure variability of returns.

c)       Covariance or variance of one asset return to other asset returns.

To generalize, higher the expected return, lower will be the standard deviation or variance and lower is the correlation. In such a case, better will be the security for investor choice. If the covariance of the securities’ returns is negative or negligible, the total risk of the portfolio of all securities may be lower as compared to the risk of the individual securities in isolation.

By developing his model, Markowitz first did away with the investment behaviour rule that the investor should maximize expected return. This rule implied that the non-diversified single security portfolio with the highest expected return is the most desirable portfolio. Only by buying that single security can expected return be maximized. The single security portfolio can be much preferred if the higher return turns out to be the actual return. However, in real world, there are conditions of so much uncertainty that most risk averse investors, joint with Markowitz in adopting diversification of securities.